Socolar-Taylor Aperiodic Tile
thingiverse
This single tile fills three-dimensional space while avoiding periodic tiling. Learn more at http://blog.makezine.com/archive/2010/03/worlds_first_aperiodic_tiling_with.html and http://maxwelldemon.com/2010/04/01/socolar_taylor_aperiodic_tile/. The blender file containing the Python code for constructing the model can be accessed at http://www.tilings.org.uk/monotile_2.blend. Use this model with a 3D printer, as two versions are provided: one with complex markings that cannot be fitted together without a fourth dimension and a simpler version that may give periodic tilings.
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